*** 10. In very-long-baseline interferometry (VLBI) tracking of interplanetary spacecraft, a 8.4-GHz radio signal is sent from a spacecraft toward the earth. In order to determine the angular position of the spacecraft, the signal is received simultaneously at two Deep Space Network (DSN) stations and the phase of the received signal at each station is measured rela- tive to a stable clock. The distance between the antenna in Australia and the one in California is 10,588,966.336 m. To spacecraft 10,588,966.336 m Australia California a) What is the wavelength of the X-band radio signal? b) If the phase of the signal in the Australia antenna is found to be 10,458.6 cycles ahead of the signal in the California antenna, what must be the angle between the direction to the spacecraft and the normal to the baseline (the dashed line in the figure above)? [Check: The answer here is 0.002°.]

*** 10. In very-long-baseline interferometry (VLBI) tracking of interplanetary spacecraft, a 8.4-GHz radio signal is sent from a spacecraft toward the earth. In order to determine the angular position of the spacecraft, the signal is received simultaneously at two Deep Space Network (DSN) stations and the phase of the received signal at each station is measured rela- tive to a stable clock. The distance between the antenna in Australia and the one in California is 10,588,966.336 m. To spacecraft 10,588,966.336 m Australia California a) What is the wavelength of the X-band radio signal? b) If the phase of the signal in the Australia antenna is found to be 10,458.6 cycles ahead of the signal in the California antenna, what must be the angle between the direction to the spacecraft and the normal to the baseline (the dashed line in the figure above)? [Check: The answer here is 0.002°.]